28,225 research outputs found
Hybrid Tractable Classes of Binary Quantified Constraint Satisfaction Problems
In this paper, we investigate the hybrid tractability of binary Quantified
Constraint Satisfaction Problems (QCSPs). First, a basic tractable class of
binary QCSPs is identified by using the broken-triangle property. In this
class, the variable ordering for the broken-triangle property must be same as
that in the prefix of the QCSP. Second, we break this restriction to allow that
existentially quantified variables can be shifted within or out of their
blocks, and thus identify some novel tractable classes by introducing the
broken-angle property. Finally, we identify a more generalized tractable class,
i.e., the min-of-max extendable class for QCSPs
Probabilistic Parsing Strategies
We present new results on the relation between purely symbolic context-free
parsing strategies and their probabilistic counter-parts. Such parsing
strategies are seen as constructions of push-down devices from grammars. We
show that preservation of probability distribution is possible under two
conditions, viz. the correct-prefix property and the property of strong
predictiveness. These results generalize existing results in the literature
that were obtained by considering parsing strategies in isolation. From our
general results we also derive negative results on so-called generalized LR
parsing.Comment: 36 pages, 1 figur
Source Coding for Quasiarithmetic Penalties
Huffman coding finds a prefix code that minimizes mean codeword length for a
given probability distribution over a finite number of items. Campbell
generalized the Huffman problem to a family of problems in which the goal is to
minimize not mean codeword length but rather a generalized mean known as a
quasiarithmetic or quasilinear mean. Such generalized means have a number of
diverse applications, including applications in queueing. Several
quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a
generalized entropy. A related property involves the existence of optimal
codes: For ``well-behaved'' cost functions, optimal codes always exist for
(possibly infinite-alphabet) sources having finite generalized entropy. Solving
finite instances of such problems is done by generalizing an algorithm for
finding length-limited binary codes to a new algorithm for finding optimal
binary codes for any quasiarithmetic mean with a convex cost function. This
algorithm can be performed using quadratic time and linear space, and can be
extended to other penalty functions, some of which are solvable with similar
space and time complexity, and others of which are solvable with slightly
greater complexity. This reduces the computational complexity of a problem
involving minimum delay in a queue, allows combinations of previously
considered problems to be optimized, and greatly expands the space of problems
solvable in quadratic time and linear space. The algorithm can be extended for
purposes such as breaking ties among possibly different optimal codes, as with
bottom-merge Huffman coding.Comment: 22 pages, 3 figures, submitted to IEEE Trans. Inform. Theory, revised
per suggestions of reader
Lowness notions, measure and domination
We show that positive measure domination implies uniform almost everywhere
domination and that this proof translates into a proof in the subsystem
WWKL (but not in RCA) of the equivalence of various Lebesgue measure
regularity statements introduced by Dobrinen and Simpson. This work also allows
us to prove that low for weak -randomness is the same as low for
Martin-L\"of randomness (a result independently obtained by Nies). Using the
same technique, we show that implies , generalizing the
fact that low for Martin-L\"of randomness implies low for
Weakened Random Oracle Models with Target Prefix
Weakened random oracle models (WROMs) are variants of the random oracle model
(ROM). The WROMs have the random oracle and the additional oracle which breaks
some property of a hash function. Analyzing the security of cryptographic
schemes in WROMs, we can specify the property of a hash function on which the
security of cryptographic schemes depends. Liskov (SAC 2006) proposed WROMs and
later Numayama et al. (PKC 2008) formalized them as CT-ROM, SPT-ROM, and
FPT-ROM. In each model, there is the additional oracle to break collision
resistance, second preimage resistance, preimage resistance respectively. Tan
and Wong (ACISP 2012) proposed the generalized FPT-ROM (GFPT-ROM) which
intended to capture the chosen prefix collision attack suggested by Stevens et
al. (EUROCRYPT 2007). In this paper, in order to analyze the security of
cryptographic schemes more precisely, we formalize GFPT-ROM and propose
additional three WROMs which capture the chosen prefix collision attack and its
variants. In particular, we focus on signature schemes such as RSA-FDH, its
variants, and DSA, in order to understand essential roles of WROMs in their
security proofs
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